4. The normal distribution Aa Aa An automobile battery manufacturer offers a 22/

Question

4. The normal distribution Aa Aa An automobile battery manufacturer offers a 22/37 warranty on its batteries. The first number in the warranty code is the free-replacement period; the second number is the prorated-credit period. Under this warranty, if a battery fails within 22 months of purchase, the manufacturer replaces the battery at no charge to the consumer. If the battery fails after 22 months but within 37 months, the manufacturer provides a prorated credit toward the purchase of a new battery The manufacturer assumes that x, the lifetime of its auto batteries, is normally distributed with a mean of 30 months and a standard deviation of 3.5 months Use the following Distributions tool to help you answer the questions that follow. (Hint: When you adjust the parameters of a distribution, you must reposition the vertical line (or lines) for the correct areas to be displayed.) Mean = 30 Standard Deviation = 5.5 10 15 20 25 30 35 40 50 2 If the manufacturer's assumptions are correct, it would need to replace of its batteries free of charge The company finds that it is replacing 1.54% of its batteries free of charge. It suspects that its assumption about the standard deviation of the life of its batteries is incorrect. A standard deviation of replacement rate results in a 1.54% Using the revised standard deviation for battery life, what percentage of the manufacturer's batteries don't qualify for free replacement but do qualify for the prorated credit? 48.46% O 95.52% 47.06% 2.94%

Explanation / Answer

1)

hence it would need to replace 1.11% of batteries free of charge.

2)

for 1.54% ; z =-2.16

therefore std deviation =(X-mean)/z =(22-30)/-2.16= 3.70

c)

for normal distribution z score =(X-)/ here mean=       = 30 std deviation   == 3.5000

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